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7.3 Proving Triangles Similar. Angle-Angle Similarity (AA ~) Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Using the AA ~ Postulate. Are the two triangles similar? How do you know? Triangle RSW and Triangle VSB.
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7.3 Proving Triangles Similar • Angle-Angle Similarity (AA ~) Postulate • If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Using the AA ~ Postulate • Are the two triangles similar? How do you know? • Triangle RSW and Triangle VSB. • Triangle JKL and Triangle PQR. a. Similar b. Not similar.
Side-Angle-Side Similarity (SAS ~) Theorem • If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar.
Side-Side-Side Similarity (SSS ~ ) Theorem • If the corresponding sides of two triangles are proportional, then the triangles are similar.
Verifying Triangle Similarity • Are the triangles similar? If so, write a similarity statement for the triangles. • Yes, Triangle STU ~ Triangle XVW by the SSS Similarity Theorem.
Verifying Triangle Similarity • Are the triangles similar? If so, write a similarity statement for the triangles. • Yes, Triangle KLP ~ Triangle KMN by the SAS Similarity Theorem.
Indirect Measurement • You can use indirect measurement to find lengths that are difficult to measure directly. • One method of indirect measurement uses the fact that light reflects off a mirror at the same angle at which it hits the mirror.
Finding the Length of Similar Triangles • Before rock climbing, Darius wants to know how high he will climb. He places a mirror on the ground and walks backward until he can see the top of the cliff in the mirror. What is the height of the cliff?
More Practice!!!!! • Homework – Textbook p. 455 – 456 # 7 – 12, 15, 16, 17.